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Article Dans Une Revue Applied Mathematics and Computation Année : 2022

Optimal control of a SIR epidemic with ICU constraints and target objectives

Résumé

The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem with SIR dynamics. The main feature of our study is the presence of state constraints (related to intensive care units ICU capacity) and strict target objectives (related to the immunity threshold). The first class of results provides a comprehensive description of different zones of interest using viability tools. The second achievement is a thorough mathematical analysis of Pontryagin extremals for the aforementioned problem allowing to obtain an explicit closed-loop feedback optimal control. All our theoretical results are numerically illustrated for a further understanding of the geometrical features and scenarios.
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Dates et versions

hal-03453722 , version 1 (28-11-2021)

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Florin Avram, Lorenzo Freddi, Dan Goreac. Optimal control of a SIR epidemic with ICU constraints and target objectives. Applied Mathematics and Computation, 2022, 418, ⟨10.1016/j.amc.2021.126816⟩. ⟨hal-03453722⟩
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